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QM: The Dilation operator

  1. Nov 24, 2011 #1
    1. The problem statement, all variables and given/known data

    Concicer the dilation operator

    [itex] D = \vec{r} * \vec{p}[/itex]

    Compute [itex] [D,\vec{r} ] and [D, \vec{p}] [/itex]

    2. Relevant equations

    [itex] p = - i * hbar [/itex]


    3. The attempt at a solution
    I think the question is really if [itex] [D, \vec{r}] [/itex] commutes

    I got this:
    [itex] D = \vec{r} * \vec{p}[/itex]
    [itex] D = x p_x + y p_y + z p_z[/itex]


    for the x direction:

    [itex][D, r] = [D, x] = [x, x p_x][/itex]

    where do i take it from here?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Nov 24, 2011 #2

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    You have absolutely no idea ?? Pick up your book and find those brackets (called <commutator>) and the properties they have.
     
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